Thursday, December 31, 2009

Knights and Knaves

A big push at my school this year is to get kids to write and to present. You know... those "21st century skills." This has never been a problem for because I am asking my kids to write explanations and present proofs and such all the time (which is probably a reason no one else wants to teach geometry). One of the ways I get my kids to write and present, while at the same time applying some if/then thinking, is through the use of Knights and Knaves logic problems. An example is as follows:
A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.You meet two inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel says, `Neither Zoey nor I are knaves.'
So who is a knight and who is a knave?
When discussing a problem like this with my students - two inhabitants, each could be a Knight or a Knave - I like my students to examine the four possible cases. By ruling out those cases that lead to contradicting statements between the inhabitants, what is left must be true (an informal introduction to proof by contradiction?).

There does seem to be somewhat of a history to these types of puzzles. These puzzles, of course, lead some of my students to The Hardest Logic Puzzle Ever, as well as to an interesting variation on the theme which introduces a "Spy" that can tell the truth or tell a lie.

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